The dynamics of an ordinary differential equations (ODEs) system modelling the interaction of four species (one prey or resource population, two mesopredator populations, and one super-predator population) was analyzed. It was assumed that the functional responses for each interaction were general. We showed parameter conditions that ensured that the differential system underwent a supercritical Hopf bifurcation or a Bogdanov-Takens bifurcation, from which the coexistence of the four species was guaranteed. In addition, the results were illustrated by several applications, where the prey had a logistic growth rate. For the interaction of the mesopredators and prey, we considered classical Holling-type functional responses, and for the rest of the interactions, we proposed certain generalized functional responses similar to the well-known "Beddington-DeAngelis" or "Crowley-Martin" functional responses. At the end, some numerical simulations were given.
Citation: Jorge Luis Ramos-Castellano, Miguel Angel Dela-Rosa, Iván Loreto-Hernández. Bifurcation analysis for the coexistence in a Gause-type four-species food web model with general functional responses[J]. AIMS Mathematics, 2024, 9(11): 30263-30297. doi: 10.3934/math.20241461
The dynamics of an ordinary differential equations (ODEs) system modelling the interaction of four species (one prey or resource population, two mesopredator populations, and one super-predator population) was analyzed. It was assumed that the functional responses for each interaction were general. We showed parameter conditions that ensured that the differential system underwent a supercritical Hopf bifurcation or a Bogdanov-Takens bifurcation, from which the coexistence of the four species was guaranteed. In addition, the results were illustrated by several applications, where the prey had a logistic growth rate. For the interaction of the mesopredators and prey, we considered classical Holling-type functional responses, and for the rest of the interactions, we proposed certain generalized functional responses similar to the well-known "Beddington-DeAngelis" or "Crowley-Martin" functional responses. At the end, some numerical simulations were given.
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Jorge Luis Ramos-Castellano, Miguel Angel Dela-Rosa, Iván Loreto-Hernández. Bifurcation analysis for the coexistence in a Gause-type four-species food web model with general functional responses[J]. AIMS Mathematics, 2024, 9(11): 30263-30297. doi: 10.3934/math.20241461
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